I didn't have any trouble eating out in Germany as a vegetarian—even the restaurants in Wernigerode had surprisingly good veggie options. Here are a few recommendations (I dunno, maybe you can bookmark this post for when you plan your own trip to Berlin?)
If you happen to stay in Kreuzberg, try Amici Miei (Mehringdamm 40), a hole-in-the-wall pizzeria with very friendly service where we got this humongous (and delicious) spinach pie for €11.80 (cheap by Irish standards). Hard to believe, but we eventually polished it off.
But our favorite eatery (we ate there twice) was Malete, on Chausseestrasse 131 in the Mitte neighborhood. The Mediterranean and Middle-Eastern-inspired dishes there were absolutely to die for—even something as simple as fried eggs over sauteed veggies with a side of roasted potatoes. Or order anything with eggplant/aubergine in it. Our meals came with a basket of the tastiest fresh toasted bread spread lightly with a parmesan/red pesto sauce. Just writing about it now makes me want to scrap the Bavaria plan and return to Berlin instead!
The last spot to recommend is in Potsdam, where I happened upon a terrific little vegetarian café close to Sanssouci called Café KieselStein (Hegelallee 23). Roasted pumpkin stuffed with feta and veggies, Asian-inspired soups made with coconut milk, homemade berry pies, organic local beers...great all-around, though the service was a bit slow. There seemed to be a lot of cute restaurants in the Dutch quarter too, but KieselStein was perfect after a long stroll through the park.